Coupling length: a generalized gleno-acetabular distance measurement for interpreting the size and gait of quadrupedal trackmakers

Abstract

The gleno-acetabular distance DGA, a conventional proxy for the size of a quadrupedal trackmaker, is often estimated as the distance GA between the midpoint between a left and right pair of pes tracks and the midpoint between a selected pair of left and right manus tracks. While frequently used to estimate trackmaker size from fossil trackways, the relationship between GA and DGA depends upon the gait (which is unknown for extinct trackmakers), and is subject to multiple additional sources of uncertainty including which specific pair of manus tracks to associate with a given pair of pes tracks. Here a generalization is introduced, termed coupling length, which does not require any presumption about trackmaker gait of the degree of overstepping. On the contrary, a systematic analysis of a trackway in terms of coupling length can permit estimation of both the size and the gait with which the trackmaker progressed. Coupling length can be computed at successive points along a trackway, allowing exploration of a range of hypothetical gaits and body sizes for the trackmaker responsible. A fitness function quantifying persistent variation in coupling length along a trackway is used to indicate whether a given trackway could have been created by a fairly consistent gait, and if so, a range of high-fitness solution gaits and their associated DGA. The method was applied to selected quasi-regular sauropod trackways and a solution found for a narrow range of gaits with limb phase of about 0.3 and DGA = 1.6 ± 0.2 m. This is the first estimation of sauropod trackmaker gait, and introduces a novel method by which irregularity along a trackway is used as a source of information to constrain inferences of trackmaker behavior. The computed DGA for this sauropod suggests significantly smaller trackmakers than conventional estimations based on track dimensions and hip height estimates. Size estimation by this approach offers greatly reduced uncertainty compared to conventional estimates.